Distinguishing a Kerr-like black hole and a naked singularity in perfect fluid dark matter via precession frequencies

Understand

We study a Kerr-like black hole and naked singularity in perfect fluid dark matter (PFDM).

• The critical value of spin parameter $a_c$ is presented to differentiate the black hole from naked singularity.
• It is seen that for any fixed value of dark matter parameter $\alpha$ the rotating object is black hole if $a\leq a_c$ and naked singularity if $a>a_c$.
• Also for $-2\leq\alpha<2/3$ the size of the black hole horizons decrease whereas for $2/3<\alpha$ it increases.